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Dissipative periodic processes


Authors: J. E. Billotti and J. P. Lasalle
Journal: Bull. Amer. Math. Soc. 77 (1971), 1082-1088
MSC (1970): Primary 34C35, 34J05; Secondary 34K15, 34K25
DOI: https://doi.org/10.1090/S0002-9904-1971-12879-3
MathSciNet review: 0284682
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  • 1. J. K. Hale, Dynamical systems and stability, J. Math. Anal. Appl. 26 (1969), 39-59. MR 39 #5896. MR 244582
  • 2. M. Slemrod, Asymptotic behavior of periodic dynamical systems on Banach spaces, Ann. Mat. Pura Appl. (to appear). MR 296464
  • 3. C. M. Dafermos, An invariance principle for compact processes, J. Differential Equations 9 (1971), 239-252. MR 291596
  • 4. M. A. Cruz and J. K. Hale, Stability of functional differential equations of neutral type, J. Differential Equations 7 (1970), 334-355. MR 41 #2166. MR 257516
  • 5. M. Slemrod and E. F. Infante, An invariance principle for dynamical systems on Banach spaces: Application to the general problem of thermoelastic stability, Proc. IUTAM Sympos. on Instability, Springer-Verlag, Berlin and New York (to appear). MR 669402
  • 6. C. M. Dafermos, Asymptotic stability in viscoelasticity, Arch. Rational Mech. Anal. (to appear). MR 281400
  • 7. M. Slemrod, Nonexistence of oscillations in a nonlinear distributed network, J. Math. Anal. Appl. (to appear). MR 282028
  • 8. J. E. Billotti, Dissipative functional differential equations, Ph.D. Dissertation, Brown University, Providence, R. I., 1969.
  • 9. Norman Levinson, Transformation theory of non-linear differential equations of the second order, Ann. of Math. (2) 45 (1944), 723-737. MR 6, 173. MR 11505
  • 10. R. Ressig, G. Sansone and R. Conti, Nichtlineare Differential gleichungen höhrer Ordnung, Edizioni Cremonese, Roma, 1969.
  • 11. V. A. Pliss, Nonlocal problems of the theory of oscillations, "Nauka", Moscow, 1964; English transl., Academic Press, New York, 1966. MR 30 #2188; 33 #4391. MR 196199
  • 12. F. E. Browder, On a generalization of the Schauder fixed point theorem, Duke Math. J. 26 (1959), 291-303. MR 21 #4368. MR 105629
  • 13. T. Yoshizawa, Ultimate boundedness of solutions and periodic solution of functional-differential equations, Colloq. Internat. Vibrations Forcées dans les Systémes Non-Linéaires, Marseilles, 1964, pp. 167-179. MR 185224
  • 14. T. Yoshizawa, Stability theory by Liapunov's second method, Publ. Math. Soc. Japan, no. 9, Math. Soc. Japan, Tokyo, 1966. MR 34 #7896. MR 208086
  • 15. G. S. Jones, Asymptotic fixed point theorems and periodic systems of functional-differential equations, Contributions to Differential Equations 2 (1963), 385-405. MR 28 #1361. MR 158135
  • 16. G. S. Jones, Periodic motions in Banach space and applications to functional differential equations with retarded arguments, Contributions to Differential Equations 3 (1963), 75-106. MR 163039
  • 17. Jack K. Hale, Synchronization by diffusive coupling, Proceedings of the Conference “Topological Methods in Differential Equations and Dynamical Systems” (Kraków-Przegorzały, 1996), 1998, pp. 17–31. MR 1661319
  • 18. J. P. LaSalle, A study of synchronous asymptotic stability, Ann. of Math (2) 65 (1957), 571-581. MR 19, 35. MR 85408
  • 19. T. Yoshizawa, Extreme stability and almost periodic solutions of functional differential equations, Arch. Rational Mech. Anal. 17 (1964), 148-170. MR 29 #3734. MR 166458
  • 20. J. P. LaSalle, Stability theory for ordinary differential equations, J. Differential Equations 4 (1968), 57-65. MR 36 #5454. MR 222402
  • 21. J. K. Hale, Geometric theory of functional-differential equations, Proc. Internat. Sympos. Differential Equations and Dynamical Systems (Mayaguez, P. R., 1965), Academic Press, New York, 1967, pp. 247-266. MR 36 #5465. MR 222413
  • 22. V. Lakshmikantham and S. Leela, Differential and integral inequalities. Vol. II, Academic Press, New York, 1969.
  • 23. J. K. Hale, Lectures on functional differential equations, University of California, Los Angeles, Calif., 1968/69.

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DOI: https://doi.org/10.1090/S0002-9904-1971-12879-3

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